When we compare how long sorting algorithms take and how much memory they use, we can look at some examples. Let’s use Merge Sort (which uses recursion) and Bubble Sort (which works iteratively).

Time Complexity

• Merge Sort: This algorithm works in a reliable way and usually takes $O(n \log n)$ time. It’s good for sorting big lists because it breaks the problem into smaller pieces and solves them.

• Bubble Sort: This one is slower, taking $O(n^2)$ time. It goes through the list many times and checks pairs of items. This makes it inefficient for large lists.

Space Complexity

• Merge Sort: It needs $O(n)$ extra space. This is because it creates temporary arrays to hold the pieces when it merges them back together.

• Bubble Sort: In comparison, Bubble Sort uses $O(1)$ space. This means it makes all the changes in the same place, using very little extra memory.

Overall Comparison

So, in summary, recursive methods like Merge Sort can be easier to understand and use. On the other hand, iterative methods like Bubble Sort can use less memory.

However, how well they perform can change based on the situation. It’s always a good idea to choose the right one based on what you need for sorting!